We are talking contract law here, as long as the French ISPs agree to the requests of the music industry and the users agree* to the terms of their internet provision then the only laws that would affect this are unfair contract and provision of services type laws. IANAL but I cannot see how a clause that states "if you misuse the service we will warn you twice and then terminate your contract" I believe my existing internet subscription contract has such a clause already but without the 2 warnings.
However, should the ISPs refuse to agree to the music industry request, as appears the case in Eire, then any enforcement of these requests would have to be through the legal channels. This is where the claim that EU and Irish law would not allow this. I assume that French Law would also not allow this, but the Frenchies voluntarily puckered up and bent over.
*If you don't like the terms go with a different ISP. If they all have the same terms then you still have a choice, you can do without any interweb connection. Or piggyback off an unsecured neighbour's wireless.